Your logic can just as easily be reversed. Amazon made an app for iPhone and iPad, so clearly they are willing to make an app for Apple TV too.
In actuality, I think Apple is not eager to introduce more competitors on their *main* TV streaming device. On iOS it doesn't matter as much, since fewer people will watch movies on their phone than on their TV.
I don't think you understand what Apple makes money from. Apple is a hardware company primarily. They make the vast bulk of their revenue from hardware sales. Look at any of their earnings reports for this. The money Apple makes from appstore cuts is relatively small compared to their hardware revenue.
On the flip side, Amazon is a services company. They make the vast bulk of their revenue from selling services - hosting, storefront, and Prime subscriptions. Again, this is supported in their earnings reports. Their hardware (kindle tablets, firetv, etc.) are pretty much loss leaders designed to get more people to buy Prime. It's all about Prime for them indeed. They don't make much money selling hardware.
Thus, while there is certainly overlap, Amazon and Apple aren't really competitors. Just like Netflix and Apple aren't really competitors. Thus, it's silly to say Apple would block Amazon to prevent a competitor.
Moreover, while Apple has been heavy handed in the past with app denials, it has been much better the past few years. The guidelines and rules are now thorough and clear. There is
no reason for Apple to deny an amazon app in their guidelines.
Other blogs that wrote about this are right: this isn't about Apple not wanting an Amazon app. This is about Amazon not wanting to give Apple a cut of their sales made inside the app, and refusing to release an app that does streaming only.